The search returns the most relevant search results based on MySQL's built-in Full Text search: http://dev.mysql.com/doc/refman/5.1/...xt-search.html
It's going to try to return the most accurate results based on whatever words are chosen.
However, the word "my" is probably not being indexed by MySQL because by default MySQL's minimum word length for an indexed word is 4 characters. So MySQL is probably ignoring the word "my" when you use it in the search. Here's more info about that: http://www.datafeedr.com/forums/showthread.php?t=1572
But to answer your question, it's not really possible to change this.